Digital tracer control

ABSTRACT

A digital tracer control responsive to inputs from a tracing head for controlling servomechanism inputs of a machine. From the tracing transducers, the system immediately converts the analogue tracing signal into a digital representation. Through the use of digital differential analyzers or modifications thereof, output pulse rates are obtained analogous to tracer error and suitable for use in machine servosystems. The system is capable of tracing a three-dimensional model in any plane within a coordinate system defined by the machine axes.

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DEPTH QUADRATURE comer/mt ROTATION/H. 9 consrmr I HODIFIER consr/mr NOOIFIER I HODIFIER 94 I 1 FEEDRATE SlNE-COSINE I Genera/man GENERATOR -10;

no I r i mueumnt uonrvu. hi-$31 whi i Sal-figs i a neuron oznznmon I i I r n r vecron I I I .rurmmo I emcurr g -.1 L -L- TEFIOJB [56] References Cited UNITED STATES PATENTS 3,283,129 1/1966 Kelling 235/15 1 .11 X 3,292,495 12/1966 Hillet a1. 235/l5l.1l X 3,300,696 1/1967 Fillmore et al 318/578 3,449,742 6/1969 Stapleton 318/578 Primary Examiner-Eugene G. Botz Assistant Examiner-Felix D, Gruber Attorneys-Howard T. Keiser and Jack .I Earl I 1 runes/I PLANE I srcmme cw I cmcurrs l F I I o vcprtow I AING I CIRCUITRY I DIGITAL l0 ANALOGUE CONVIRTEHS genvo J UMHING uervonne SERVO mrunens DRIVE ELIHZNTS FEEDBACK UNHS PATH-HEB SEP28 IQTI 3 Q 09 ,322

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HAROLD D. WI EBE BY T NEYS PATEHTEDSEP28|9H 3,609,322

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cmculmY DlGlTAL TO 324 33 33a /ANALO6UE coNvERnRs SERVO r //37 SUMMING 335 337 339 NETWORKS I l AMPLIFIERS 340 342 344 g ix g lfib I22 I30 sfjg 4a 60 74 I39 FEEDRATE l/lo VELOCITY VECTOR NORMAL YEL8CITTY 98 EC on 104 IOI 0, 7 PATTERN PATEi-HEUSEP28|nrl 3.509.322

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sumMmca NETWORKS CONVERTERS PATEI'HED SEP28 I87! SHEET (38 [1F 17 HANG FREE POSITION SYSTEM NULL DEFINED PARALLEL OUTPUT DIGITAL COUNTER Mia; OVERDEFLECT'ON UNDERDEFLECTION INPUT A Z sum/mFr-snenca INPUT sum DIFFERENCE INPUT 3 CARRY/BORROW TRIGGER VFL FULL ADDER/SUBTRACTOR our. BIT ADDER/SUBTHACTOR m PUT A 'NPUT OUTPUT G OUTPUT nalvme FUNCTION STORAGE HEmsTER GATE INPUT SERIAL OUTPUT INPUT OUTPUT FUNCTION BLOCK PATENTED SEP28 I97! sum 12 or 17 PATENTEB SEP28 I97! 3,609,322

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PATENTED SEFZ 8 I971 SHEET 1U [1F 17 DIGITAL TRACER CONTROL BACKGROUND Other tracer systems use discrete component analogue circuits that are subject to several inherent disadvantages. These tracing systems are controlled by changing the magnitude and phase of an error signal continuous in time. A major problem is drift of circuit parameters that causes erratic operation of the machine and resulting inaccuracies in the trace. Further, the critical nature of analogue circuits requires that they be adjusted to operate in a relatively narrow tracing velocity range. Consequently a wide range of materials cannot be accurately cut on the same machine.

This invention proposes a tracing system in which the method for creating a signal analogous to tracing error and continuous in time is improved. In addition, the application of a digital control to three-dimensional tracing is new. By using a digital control the problem of drift is eliminated; therefore, accuracies are improved. Second, a digital control provides system stability throughout a wide range of tracing velocities. Third, the high speed and reliability inherent in a digital control facilitates interfacing with recording devices, computers and standard machine servo mechanisms. Finally, a digital design allows the use of microcireuits and a smaller more reliable package may be developed.

Conventional tracers have three modes of operation. First, the Depth Mode, or single dimensional tracing provides a tracer response in a direction parallel to the longitudinal axis of a tracing head. Second, the Planar Mode, or two-dimensional tracing is the ability to trace in a plane parallel to one of the coordinate planes defined by the machine axes. When a three-dimensional contour has to be traced, the Combination Mode is used. In this mode,-it is necessary to separate the contour into two independent tracing paths. First, the planar path represents a planar slice of the contour perpendicular to the longitudinal axis of a tracing head. Second, the depth path represents changes at the point of the planar slice in a direction parallel to the longitudinal axis of a tracing head. The planar and depth paths are simultaneously tracked, processed by independent tracer control circuits and transmitted to their respective machine tool axes.

There are two major disadvantages to tracing in the Combination Mode. First, there are geometric limitations. The model must have contours that can readily be defined by depth and planar paths. in addition, the type of tracing head may limit the rate of change of depth with respect to a planar slice. Second, there is no control over the feedrate in the depth direction; it is a function of error. ln the Combination Mode, tracing is the result of two feedrate vectors. First, the planar vector is determined by the feedrate selected by the operator and controls the tracing rate along the planar path. Second, the depth vector is determined by the depth error and can not be controlled externally. This assumes that the system response in the depth direction will be able to follow the selected feedrate.

To overcome the disadvantages of conventional tracers, this invention teaches the Plane Steering Mode as the best means of tracing in three dimensions. Plane steering is a two-dimensional tracing mode with the ability to steer the tracing plane about a contour. Thus, the tracing plane is always approximately normal to the surface being traced. Plane steering is selected by the operator; who, by manual controls, has the ability to rotate the tracing plane about one or more of the coordinate axes. This is accomplished in the tracer control which then translates motion in the new plane into resultant velocity vectors parallel to the axes of motion of the machine. Consequently, models can be traced directly with no need to make special patterns or templates.

Accordingly, this invention provides for a reliable high speed digital tracer control that eliminates drift problems and allows tracing in a wide range of velocities. Consequently, tracing in the Depth, Planar, and Combination Modes is improved. Further, the Plane Steering Mode permits direct tracing in any plane within the machine coordinate system.

SUMMARY This invention is most applicable to a tracing head mounted in a standard machine tool configuration. The digital tracer control receives inputs provided by the operator in combination with error signals form the tracing head and transmits command pulse rates to the machine servo system. The servo system then moves the machine slides at the commanded velocities so as to decrease the error detected by the tracing head.

A tracing finger in physical contact with the model imparts a deflection to transducers. The transducers provide a continuous electrical signal analogous to deflection. An analogue to digital converter converts the continuous electric signal to a digital error signal representing a number word having a value proportional to deflection. The digital error signal is synchronized with the tracer control in a synchronization circuit by modifying a constant pulse rate from a clock oscillator proportionally to the number word value. The modified pulse rate provides for the generation of normal and rotational system response signals to the tracking of the tracing finger. The rotational response signal drives two digital integrators connected so as to provide a sine-cosine generator. The generator produces output signals which are digital representations of the sine and cosine magnitudes of the angle of rotation. The sine and cosine magnitudes are used to redefine two tracing vectors into two new usable vector quantities. The first tracing vector, feedrate vector, is tangential to the tracing path at the point of the trace. The second tracing vector, quadrature vector, has a direction normal to the tracing path at the point of the trace, and its magnitude is proportional to tracing error. The feedrate vector and the quadrature vector define a tracing plane. The rotational system generates vector components by projecting each tracing-vector onto axes, in the tracing plane, parallel to the machine axes. The corresponding vector components are summed to produce two new vectors. The steering system allows a first rotation of the tracing plane about a coordinate axis parallel to either one of the axes defined by the two new vectors. The plane may be rotated a second time about a coordinate axis perpendicular to the first rotational axis. This permits the tracing plane to be skewed within the coordinate system defined by the machine axes. The angles of steering are measured in terms of their trigonometric magnitudes. These magnitudes are used to project the two new vector outputs of the rotational system onto coordinate axes. The projection generates vector components which are summed to produce command velocity vectors parallel to the coordinate axes. These command vectors are gated to the appropriate servo mechanism inputs to move the machine slides at the desired velocities and in a direction to decrease the error detected by the tracing head.

DESCRlPTlON OF DRAWINGS While the invention has been illustrated in some detail according to a preferred embodiment shown in the accompanying drawings, and while the preferred illustrated embodiment will be described in some detail, there is no intention to thus limit the invention to such details. On the contrary, it is intended to cover all modifications, alternations and equivalents falling within the spirit and scope of the appended claims. In the block and schematic diagrams, the solid lines interconnecting the various elements are only indicative of signal flow. Consequently, a line may signify one or more conductors, each carrying a specific signal. The uniform dashed lines represent mechanical connections. The combined long and short dashed lines define specific combinations of elements.

FlGS. la, lb, 1c and Id, graphically show the abilities and limitations of the four tracing modes.

FIG. 2 is a perspective view of a machine which may be controlled according to he method and apparatus of the present invention.

FIGS. 30 and 311 when joined along the indicated junction line, represent the functional block and line diagram of the entire control system.

FIGS. 3c and 3d when joined along the indicated junction line, represent the functional block and line diagram of an alternative embodiment of the control system.

FIG. 4 is a representation of the error quantities that exist at the point of the trace and is an aid to understanding the rotational system.

FIGS. 5a, 5b, 5c, and 5d, graphically illustrate the hang-free to null deflection, system null, and deflection about the system null.

FIGS. 6a, 6b, 6c, 6d, 6e, and 6f, are keys to explain the meaning of the symbols used in the detailed schematic diagrams.

FIGS. 7a, 7b, 7c, 7d, 72, and 7f, when joined along the indicated junction line, comprise a detailed schematic diagram of the entire digital tracer control.

FIGS. 7bl, 7cl, and 762, comprise a detailed schematic diagram of an alternative embodiment and should bejoined along the indicated junction lines with FIGS. 7a, 7d, 7e, and 7f.

GENERAL DESCRIPTION Before proceeding with the circuit descriptions, a further expansion of tracing philosophies is necessary.

FIGS. la illustrates one dimensional tracing in the Depth Mode. After studying the model 12, the operator must select coordinate directions that define a family of parallel planes in which the desired contour may be traced. In this case, the selected coordinate directions are along the X-axis 10 and the Z-axis 14. The family of parallel planes progress perpendicular to the Y-axis 11. The operator must then select the tracing feedrate and initiate the trace. The tracing finger 13 will detect error in a direction parallel to the Z-axis 14. The selected feedrate and the tracing error respectively determine the constant feedrate vector 8 and the error vector 9. These two vectors define the tracing plane 17 at any given time.

Tracing in two dimensions, or in the Planar Mode is shown in FIG. lb. In this case, the operator will select coordinate directions along the X-axis l0 and the Y-axis 11 to define a family of planes perpendicular to the Z-axis 14. The tracing plane 17 is defined by the feedrate vector 15 and the quadrature vector 16, which originate at the point of contact between the tracing finger l3 and the model 12. FIG. 10 illustrates the historic method of tracing in three dimensions or the Combination Mode. In this case, the operator selects a feedrate and coordinate directions the same as in the Planar Mode.

However, since there are two independent tracing paths and two points of contact on the tracing finger 13, two sets of response vectors will exist. The feedrate vector 15 and the quadrature vector 16 define the tracing plane 17a. The feedrate vector 15 and the error vector 9 define a second tracing plane 17b. The responses in each tracing plane 170 and 17b are processed in independent systems and routed to the appropriate machine servo mechanisms to produce simultaneous three axis motion.

The newest and most practical tracing mode, uniquely taught by this invention, is illustrated in FIG. 1d. There may be many surfaces on a model that cannot be accurately traced with a tracing plane that is parallel to one of the coordinate planes. The Plane Steering Mode overcomes this problem. First, the operator selects a set of coordinate directions and a feedrate as previously described. This establishes a family of tracing planes parallel to the coordinate plane defined by the selected coordinate directions. By plane steering controls, the operator can rotate these planes about the coordinate axes. In effect, the operator can steer the tracing planes within the coordinate system until it is approximately perpendicular to the surface to be traced. Such a position provides for the most accurate tracing. FIG. ld shows a model 12 in a skewed position. Assume the operator chose the X-axis I0 direction and the Y-axis I1 direction. This defines a family of planes perpendicular to the Z-axis 14. Then he steers the plane through a first angle 18 and a second angle 19. The fecdrate vector 15 and the quadrature vector 16 define a specific tracing plane 17 approximately perpendicular to the surface being traced. Hence, the plane steering mode gives the operator the ability to directly trace complex models. Consequently, cost savings are realized in not having to make special patterns.

For purposes of illustration, FIG. 2 shows the tracer on a traveling column, bar-type milling machine with a hydraulic drive system. It is to be understood the tracing apparatus may be adapted to other machine configurations and other drive systems. The machine illustrated consists of a bed 28 with ways 30 on its top surface. The ways 30 run in a direction perpendicular to the surface of the paper as viewed by the reader. Supported on the bed 28 is a vertical column 32. Fastened to its bottom surface are slides 34 that mate with the ways 30 of the bed 28. A hydraulic motor 36 is mechanically connected through driving members 38 and 40 to a pinion 42. The pinion 42 by pushing against a rack 44 drives the column 32 along the longitudinal axis of the bed 28. This action is initiated by an electrical analogue signal transmitted to a hydraulic servo valve 46. The servo valve 46 controls the flow of fluid into the hydraulic motor 36. A feedback device 48 is mechanically connected to the hydraulic motor 36 to detect its movement. Mounted on top of the column 32 is a servo valve 50 identical to the other valve 46. The servo valve 50 controls the fluid flow to the hydraulic motor 52 which drives a ball screw 54. Mounted on a nut 56 of the ball screw 54 is a carrier 58. Mounted on a hydraulic motor 52 and detecting the vertical motion of the carrier 58 is another feedback device 60.

Fastened to the carrier 58 are vertical slides 62 that mate with the vertical ways 64 on the column 32. Centrally located on the surface of the carrier 58, facing the reader, are ways 66 and a ball screw 68. Connected to the ball screw 68 is a hydraulic motor 70 which is controlled by a servo valve 72, Detecting motion of the ball screw 68 is a feedback device 74. Mounted on the nut 76 of the ball screw 68 is a spindle housing 78. The ball screw 68 provides motion in a direction mutually perpendicular to the longitudinal and vertical movements previously described. The spindle housing 78 is guided by slides 80 which mate with the ways 66 on the carrier 58. Mounted in the end of the spindle housing 78 is the tracing unit 82. The model I2 is mounted on an angle plate 84 that is on a base 85 opposite the tracing finger 13.

There are several methods known in the tracer art to detect the contour of a model. For example, mechanical. optical. or sonic techniques may be used. For purposes of this disclosure, the tracing head has a transducer that translates the output of the detection system in to an analogue error signal. Through a given increment of motion, the error signal magnitude represents the difference between the actual position of the tracing finger and the theoretical position as determined by the contour of the model. The tracing head, used in this system, is an electromechanical model that is thoroughly described in US. Pat. No. 2,868,087 issued to .l. M. Morgan, Jr. on .Ian. 13, 1959.

FIGS. 30 and 3b when joined along the indicated junction line represent a functional block diagram of one embodiment of the tracer control system, It should be remembered that the general description portion of the specification is functional in nature to aid in the understanding of the whole tracer control. Each important block of FIG. 3 will be structurally defined and its operation explained later in the description of opera tion. The tracer control of FIGS. 3c, and 3d is identical to the tracer control of FIGS. 3a and 3b with the exception that an improved configuration of elements is provided in the depth system for tracing in the Combination Mode.

In the system of FIG. 3a, the tracing head 82 detects the presence of a model by means of a the rotational finger l3. Mechanically connected to the tracing finger [3 are transducers 86. The transducers 86 provide planar deflection signal continuous in time and analogous to the total tracing finger deflection. An analogue to digital converter 90 converts the analogue planar deflection signal into an error signal representing a binary expression as a function of to the planar deflection signal magnitude. The converter 90 contains a zero 

1. An automatic control apparatus for producing drive signals to servomechanism inputs of three movable elements having three mutually perpendicular axes of motion defining a rectangular coordinate system, said drive signals being initiated by applying error signals from a tracing head to the control apparatus, said error signals include a depth signal representing tracing error detected in a direction parallel to one axis of the coordinate system and a planar signal representing tracing error detected in a plane perpendicular to the one axis, the apparatus comprising: a. means for providing a constant frequency serial stream of pulses; b. means responsive to the error signals and the serial stream of pulses for producing a serial train of pulses having a frequency that is a function of the magnitude of the error signals; c. means for generating digital signals representing sine and cosine values of a tracing angle of rotation, said generating means being response to the serial train of pulses for incrementally changing the digital signals; d. means for supplying a variable pulse rate adjustable in time and representing a predetermined tracing velocity magnitude; and e. a cyclically operable pulse generator responsive to the serial train of pulses, the digital signals and the variable pulse rate for generating the drive signals for the servomechanism inputs.
 2. An automatic control apparatus for producing drive signals to servomechanism inputs of three movable elements having three mutually perpendicular axes of motion defining a rectangular coordinate system, said drive signals being initiated by applying error signals from a tracing head to the control apparatus, said error signals include a depth signal representing a tracing error detected in the direction parallel to one axis of the coordinate system and a planar signal representing a tracing error detected in plane perpendicular to the one axis, the apparatus comprising: a. means for providing a constant frequency serial stream of pulses; b. means responsive to the error signals and the serial stream of pulses for producing a first serial train of pulses having a frequency proportional to the depth signal magnitude and a second serial train of pulses having a frequency proportional to the planar signal magnitude; c. means responsive to the planar signal and the second serial train of pulses for generating digital planar signals representing sine and cosine values of a planar angle of rotation; d. means for supplying a variable pulse rate adjustable in time and representing a predetermined tracing velocity magnitude; e. means responsive to the digital planar signals and the seconD serial train of pulses for producing a first pulse string by scaling the second serial train of pulses as a function of the sine value of the planar angle of rotation and a second pulse string by scaling the second serial train of pulses is a function of the cosine value of the planar angle of rotation; f. means responsive to the digital planar signals and the variable pulse rate for producing a first serial pulse string by scaling the variable pulse rate as a function of the cosine value of the planar angle of rotation and a second serial pulse string by scaling the variable pulse rate as a function of the sine value of the planar angle of rotation; g. means responsive to the pulse strings and the serial pulse strings for summing the first pulse string with the first serial pulse string to produce a first string of pulses and the second pulse string with the second serial pulse string to produce a second string of pulses; h. means having inputs responsive to the digital planar signals the strings of pulses, the depth signal, and the first serial train of pulses for combining the inputs to produce trains of pulses; and i. means responsive to the trains of pulses for selectively producing a first drive signal output for reducing the error represented by the depth signal and a second drive signal output for reducing the error represented by the planar signal.
 3. An automatic control apparatus for producing drive signals to servomechanism inputs of three movable elements having three mutually perpendicular axes of motion defining a rectangular coordinate system, said drive signals being initiated by applying error signals from a tracing head to the control apparatus, said error signals include a depth signal representing a tracing error detected in the direction parallel to one axis of the coordinate system and a planar signal representing a tracing error detected in a plane perpendicular to the one axis, the apparatus comprising: a. a clock oscillator for providing a constant frequency serial stream of pulses; b. a synchronizing network responsive to the error signals and the serial stream of pulses for producing a first signal train of pulses by rate multiplying the serial stream of pulses by a magnitude represented by the depth signal and a second serial train of pulses by rate multiplying the serial stream of pulses by a magnitude represented by the planar signal; c. a first digital gain network responsive to the second serial train of pulses for rate multiplying the second serial train of pulses by two signals representing predetermined constant values and producing two pulse streams; d. means responsive to one of the pulse streams and the planar signal for generating digital planar signals representing sine and cosine values of a planar angle of rotation; e. a second digital gain network responsive to the first serial train of pulses for rate multiplying the first serial train of pulses by signal representing a predetermined constant value and producing a serial pulse streams; f. an adjustable feedrate oscillator for supplying a variable pulse rate adjustable in time and representing a predetermined tracing velocity magnitude; g. a first set of two rate multiplication circuits, each circuit having a first input connected to the other of the pulse streams, one of the circuits having a second input responsive to the digital planar signal representing the sine value of the planar angle of rotation and the other circuit having a second input responsive to the digital planar signal representing the cosine value of the planar angle of rotation, said circuits producing two pulses strings; b. a second set of two rate multiplication circuits, each circuit having a first input responsive to the variable pulse rate, one of the circuits having a second input responsive to the digital planar signal representing the sine value of the planar angle of rotation and the other of circuits having a second input responsive to thE digital planar signal representing the cosine value of the planar angle of rotation, said circuits producing two serial pulse strings; i. an adder storage network having inputs responsive to the pulse strings and the serial pulses strings for producing two strings of pulses; j. a gating network having inputs responsive to the digital planar signals, the strings of pulses, the depth signal and the serial pulse stream for switching the inputs to produce trains of pulses; and k. a switching network responsive to the trains of pulses for selectively producing a first drive signal output for reducing the error represented by the depth signal and a second drive signal output for reducing the error represented by the planar signal.
 4. An automatic control apparatus for producing drive signals to servomechanism inputs of three movable elements having three mutually perpendicular axes of motion defining a rectangular coordinate system, said drive signals being initiated by applying error signals from a tracing head to the control apparatus, said error signals include a depth signal representing a tracing error detected in a direction parallel to one axis of the coordinate system and a planar signal representing a tracing error detected in a plane perpendicular to the one axis, the apparatus comprising: a. means for providing a constant frequency serial stream of pulses; b. means responsive to the error signals and the serial stream of pulses for producing a first serial train of pulses having a frequency proportional to the depth signal magnitude and a second serial train of pulses having a frequency proportional to the planar signal magnitude; c. means responsive to the planar signal and the second serial train of pulses for generating digital planar signals representing sine and cosine values of a planar angle of rotation; d. means for supplying a variable pulse rate adjustable in time and representing a predetermined tracing velocity magnitude; e. means responsive to the first serial train of pulses and the depth signal for producing digital depth signals representing sine and cosine values of a depth angle of rotation; f. means responsive to the digital depth signals and the first serial train of pulses for producing a first pulse rate by scaling the first serial train of pulses as a function of the cosine value of the depth angle of rotation and a second pulse rate by scaling the first serial train of pulses as a function of the sine value of the depth angle of rotation; g. means responsive to the digital depth signals and the variable pulse rate for producing a first serial pulse rate by scaling the variable pulse rate as a function of the sine value of the depth angle of rotation and a second serial pulse rate by scaling the variable pulse rate as a function of the cosine value of the depth angle of rotation; h. means responsive to the digital depth signals, the pulse rates and the serial pulse rates for algebraically summing the first pulse rate with the first serial pulse rate to produce a first serial string of pulses and the second pulse rate with the second serial pulse rate to produce a second serial string of pulses; i. means responsive to the digital planar signals and the second serial train of pulses for producing a first pulse string by scaling the second serial train of pulses as a function of the sine value of the planar angle of rotation and a second pulse string by scaling the second serial train of pulses as a function of the cosine value of the planar angle of rotation; j. means responsive to the digital planar signals and the second serial string of pulses for producing a first serial pulse string by scaling the second serial string of pulses is a function of the cosine value of the planar angle of rotation and a second serial pulse string by scaling the second serial string of pulses as a function of the sine value of the planar angle of rotation; k. means responsive to the pulse striNgs and the serial pulse strings for summing the first pulse string with the first serial pulse string to produce a first string of pulses and the second pulse string with the second serial pulse string to produce a second string of pulses; and l. means having inputs responsive to the digital planar signals, the first serial string of pulses and the strings of pulses for combining the inputs to produce the drive signals for the servomechanism inputs.
 5. An automatic control apparatus for producing drive signals to servomechanism inputs of three movable elements having three mutually perpendicular axes of motion defining a rectangular coordinate system, said drive signals being initiated by applying error signals from a tracing head to the control system, said errors signals include a depth signal representing a tracing error detected in a direction parallel to one axis of the coordinate system and a planar signal representing a tracing error detected in a plane perpendicular to the one axis, the apparatus comprising: a. a clock oscillator providing a constant frequency serial stream of pulses; b. a synchronizing network responsive to the error signals and the serial stream of pulses for producing a first serial train of pulses by rate multiplying the serial stream of pulses by the magnitude represented by the depth signal and a second serial train of pulses by rate multiplying serial stream of pulses by the magnitude represented by the planar signal; c. a first digital gain network responsive to the second serial train of pulses for rate multiplying the second serial train of pulses by two signals representing predetermined constant values and producing two pulses streams; d. means responsive to one of the pulse streams and the planar signal for generating digital planar signals representing sine and cosine values of a planar angle of rotation; e. a second digital gain network responsive to the first serial train of pulses for rate multiplying the first serial train of pulses by two signals representing predetermined constant values and producing two serial pulses streams; f. an adjustable feed rate oscillator for supplying a variable pulse rate adjustable in time and representing a predetermined tracing velocity magnitude; g. means responsive to one of the serial pulse streams and the depth signal for producing two digital depth signals representing sine and cosine values of a depth angle of rotation; h. a first set of two rate multiplication circuits, each circuit having a first input responsive to the other of the serial pulse streams, one of the circuits having a second input responsive to the digital depth signal representing the sine value of the depth angle of rotation and the other circuit having a second input responsive to the digital depth signal representing the cosine value of the depth angle of rotation, said circuits producing two pulse rates; i. a second set of two rate multiplication circuits, each circuit having a first input responsive to the variable pulse rate, one of the circuits having a second input responsive to the digital depth signal representing the sine value of the depth angle of rotation and the other circuit having a second input responsive to the digital depth signal representing the cosine value of the depth angle of rotation, said circuits producing two serial pulse rates; j. an adder/subtracter circuit having inputs responsive to the digital depth signals, the pulse rates and the serial pulse rates for producing two serial strings of pulses; k. a third set of two rate multiplication circuits, each circuit having a first input connected to the other of the pulse streams, one of the circuits having a second input responsive to the digital planar signal representing the sine value of the planar angle of rotation and the other circuit having a second input responsive to the digital planar signal representing the cosine value of the planar angle of rotation, said circuits producing two puLses strings; l. a fourth set of two rate multiplication circuits, each circuit having a first input responsive to one of the serial strings of pulses, one of the circuits having a second input responsive to the digital planar signal representing the sine value of the planar angle of rotation and the other of the circuits having a second input responsive to the digital planar signal representing the cosine value of the planar angle of rotation, said circuits producing two serial pulse strings; m. an adder storage network having inputs responsive to the pulse strings and the serial pulse strings for producing two strings of pulses; and n. gating network having inputs responsive to the digital planar signals, the other of the serial strings of pulses and the strings of pulses for switching the inputs to produce the drive signals for the servomechanism inputs.
 6. An automatic control apparatus for producing drive signals to servomechanism inputs of three movable elements having three mutually perpendicular axes of motion defining a rectangular coordinate system, said drive signals being initiated by applying error signals from a tracing head to the control apparatus, said error signals include a depth signal representing a tracing error detected in the direction parallel to one axis of the coordinate system and a planar signal representing a tracing error detected in a plane perpendicular to the one axis, the apparatus comprising: a. means responsive to the error signals for summing said signals to produce a resultant error signal representing the magnitude of the total tracing error; b. means for providing a constant frequency serial stream of pulses; c. means responsive to the resultant error signal and the serial stream of pulses for producing a serial train of pulses having a frequency proportional to the magnitude of the resultant error signal; d. means responsive to the resultant error signal and the serial train of pulses for generating digital planar signals representing sine and cosine values of a planar angle of rotation; e. means for supplying a variable pulse rate adjustable in time and representing a predetermined tracing velocity magnitude; f. means responsive to the digital planar signals and the serial train of pulses for producing a first pulse string by scaling the serial train of pulses as a function of the sine value of the planar angle of rotation and a second pulse string by scaling the serial train of pulses as a function of the cosine value of the planar angle of rotation; g. means responsive to the digital planar signals and the variable pulse rate for producing a first serial pulse string by scaling the variable pulse rate as a function of the cosine value of the planar angle of rotation and a second serial pulse string by scaling the variable pulse rate as a function of the sine value of the planar angle of rotation; h. means responsive to the pulse strings and the serial pulse strings for summing the first pulse string with the first serial pulse string to produce a first string of pulses and the second pulse string with the second serial pulse string to produce a second string of pulses; i. means for generating digital steering signals representing sine and cosine values of a steering angle of rotation; j. means responsive to the digital steering signals and one of the strings of pulses for producing a first pulse train by scaling the one of the strings of pulses as a function of the sine value of the steering angle of rotation and a second pulse train by scaling the one of the strings of pulses as a function of the cosine value of the steering angle of rotation; and k. means having inputs responsive to the digital planar signals, the digital steering signals, the other of the strings of pulses and the pulse trains for combining the inputs to produce the drive signals for the servomechanism inputs.
 7. An automatic control apparatus for producing drive signals to servomechaniSm inputs of three movable elements having three mutually perpendicular axes of motion defining the rectangular coordinates system, said drive signals being initiated by applying error signal from a tracing head to the control apparatus said, error signals include a depth signal representing a tracing error detected in a direction parallel to one axis of the coordinate system and a planar signal representing a tracing error detected in a plane perpendicular to the one axis, the apparatus comprising: a. a phase shift network responsive to the depth signal for shifting the phase of the depth signal one quarter of a period in time; b. a gating network responsive to the phase shifted depth signal for switching the phase shifted depth signal in series with the planar signal to produce a resultant error signal representing the magnitude of the total tracing error; c. a clock oscillator for providing a constant frequency serial stream of pulses; d. a synchronizing network responsive to the resultant error signal and the serial stream of pulses for producing a serial train of pulses by rate multiplying the serial stream of pulses by the magnitude of resultant error signal; e. a digital gain network responsive to the serial train of pulses for producing two pulse streams by rate multiplying the serial train of pulses by two signals representing predetermined constant values; f. means responsive to the resultant error signal and one of the pulse streams for generating digital planar signals representing sine and cosine values of a planar angle of rotation; g. an adjustable feed rate oscillator for supplying a variable pulse rate adjustable in time and representing a predetermined tracing velocity magnitude; h. a first set of two rate multiplication circuits, each circuit having a first input responsive to the other of the pulse streams, one of the circuits having a second input responsive to the digital planar signal representing the sine value of the planar angle of rotation and the other circuit having a second input responsive to the digital planar signal representing the cosine value of the planar angle of rotation, said circuits producing two pulse strings; i. a second set of two rate multiplication circuits, each circuit having a first input responsive to the variable pulse rate, one of the circuits having a second input responsive to the digital planar signal representing the cosine value of the planar angle of rotation and the other circuit having a second input responsive to the digital planar signal representing the sine value of the planar angle of rotation, said circuits producing two serial pulse strings; j. an adder storage network having inputs responsive to the pulse strings and the serial pulses strings for producing two strings of pulses; k. a manually operable transducer circuit for producing digital steering signals representing sine and cosine values of a steering angle of rotation; l. a third set of two rate multiplication circuits, each circuit having a first input responsive to one of the strings of pulses, one of the circuits having a second input responsive to the digital steering signal representing the sine value of the steering angle of rotation and the other of the circuits having a second input responsive to the digital steering signal representing the cosine value of the steering angle of rotation, said circuits producing two pulse trains; and m. a gating network having inputs responsive to the digital planar signals, the digital steering signals, the other of the strings of pulses and the pulse trains for switching the inputs to produce the drive signals for the servomechanism inputs.
 8. An automatic control apparatus for producing drive signals to servomechanism inputs of three movable elements having three mutually perpendicular axes of motion defining a rectangular coordinate system, said drive signals being initiated by applying error signals from a tracing head to the control appAratus, said error signals include a depth signal representing a tracing error detected in a direction parallel to one axis of the coordinate system and a planar signal representing a tracing error detected in a plane perpendicular to the one axis, the apparatus comprising: a. means responsive to the error signals for summing said signals to produce a resultant error signal representing the magnitude of the total tracing error; b. means for providing a constant frequency serial stream of pulses; c. means responsive to the resultant error signal and the serial stream of pulses for producing a serial train of pulses having a frequency proportional to the magnitude of the resultant error signal; d. means responsive to the resultant error signal and the serial train of pulses for generating digital planar signals representing sine and cosine values of a planar angle of rotation; e. means for supplying a variable pulse rate adjustable in time and representing a predetermined tracing velocity magnitude; f. means responsive to the digital planar signals and the serial train of pulses for producing a first pulse string by scaling the serial train of pulses as a function of the sine value of the planar angle of rotation and a second pulse string by scaling the serial train of pulses as a function of the cosine value of the planar angle of rotation; g. means responsive to the digital planar signals and the variable pulse rate for producing a first serial pulse string by scaling the variable pulse rate as a function of the cosine value of the planar of rotation and a second serial pulse string by scaling the variable pulse rate as a function of the sine value of the planar of rotation; h. means responsive to the pulse strings and the serial pulse strings for summing the first pulse string with the first serial pulse string to produce a first string of pulses and the second pulse string with the second serial pulse string to produce a second string of pulses; i. means for generating a first set of digital steering signals representing sine and cosine values of a first steering angle of rotation; j. means responsive to the first set of digital steering signals and one of the strings of pulses for producing a first pulse train by scaling the one of the strings of pulses as a function of the sine value of the first steering angle of rotation and a second pulse train by scaling the one of the strings of pulses as a function of the cosine value of the first steering angle of rotation; k. means for generating a second set of digital steering signals representing sine and cosine values of a second steering angle of rotation; l. means responsive to the second set of digital steering signals and the other of the strings of pulses for producing a first serial pulse train by scaling the other of the strings of pulses as a function of the sine value of the second steering angle of rotation and a second serial pulse train by scaling the other of the strings of pulses as a function of the cosine value of the second steering angle of rotation; m. means responsive to the second set of digital steering signals and one of the pulse trains for producing a third serial pulse train by scaling the one of the pulse trains as a function of the sine value of the second steering angle of rotation and a fourth serial pulse train by scaling the one of the pulse trains as a function of the cosine value of the second steering angle of rotation; and n. means having inputs responsive to the digital planar signals, the digital steering signals, the other of the pulse trains and the serial pulse trains for combining the inputs to produce the drive signals for the servomechanism inputs.
 9. An automatic control apparatus for producing drive signals to servomechanism inputs of three movable elements having three mutually perpendicular axes of motion defining a rectangular coordinate system, said drive signals being initiated by applying error signals from a Tracing head to the control apparatus, said error signals include a depth signal representing a tracing error detected in a direction parallel to one of the axes of the coordinate system and a planar signal representing a tracing error detected in a plane perpendicular to the one axis, the system comprising: a. a phase shift network responsive to the depth signal for shifting the phase of the depth signal one quarter of a period in time; b. a gating network responsive to the phase shifted depth signal for switching the phase shifted in series with the planar signal to produce a resultant error signal representing the magnitude of the total tracing error; c. a clock oscillator for providing a constant frequency serial stream of pulses; d. a synchronizing network responsive to the resultant error signal and the serial stream of pulses for producing a serial train of pulses by rate multiplying the serial stream of pulses by the magnitude represented by the resultant error signal; e. a digital gain network responsive to the serial train of pulses for producing two pulse streams by rate multiplying the serial train of pulses by two signals representing predetermined constant values; f. means responsive to the resultant error signal and one of the pulse streams for generating digital planar signals representing sine and cosine values of a planar angle of rotation; g. an adjustable feed rate oscillator for supplying a variable pulse rate adjustable in time and representing a predetermined tracing velocity magnitude; h. a first set of two rate multiplication circuits, each circuit having a first input responsive to the other of the pulse streams, one of the circuits having a second input responsive to the digital planar signal representing the sine value of the planar angle of rotation and the other circuit having a second input responsive to the digital planar signal representing the cosine value of the planar angle of rotation, said circuits producing two pulse strings; i. a second set of two rate multiplication circuits, each circuit having a first input responsive to the variable pulse rate, one of the circuits having a second input responsive to the digital planar signal representing the cosine value of the planar angle of rotation and the other circuit having a second input responsive to the digital planar signal representing the sine value of the planar angle of rotation, said circuits producing two serial pulse strings; j. an adder storage network having inputs responsive to the pulse strings and the serial pulses strings for producing two strings of pulses; k. a first manually operable transducer circuit for producing a first set of digital steering signals representing sine and cosine values of a first steering angle of rotation; l. a third set of two rate multiplication circuits, each circuit having a first input responsive to one of the strings of pulses, one of the circuits having a second input responsive to the digital steering signal representing the sine value of the first steering angle of rotation and the other circuit having a second input responsive to the digital steering signal representing the cosine value of the first steering angle of rotation, said circuits producing pulse trains; m. a second manually operable transducer circuit for producing a second set of digital steering signals representing sine and cosine values of a second steering angle of rotation; n. a fourth set of two rate multiplication circuits, each circuit having a first input responsive to the other of the strings of pulses, one of the circuits having a second input responsive to the digital steering signal representing the sine value of the second steering angle of rotation and the other circuit having a second input responsive to the digital steering signal representing the cosine value of the second steering angle of rotation, said circuits producing serial pulse trains; o. a fifth set of two rate multiplication Circuits, each circuit having a first input responsive to one of the pulse trains, one of the circuits having a second input responsive to the digital steering signal representing the sine value of the second steering angle of rotation and the other circuit having a second input responsive to the digital steering signal representing the cosine value of the second steering angle of rotation, said circuits producing serial pulse trains; and p. a gating network having inputs responsive to the digital planar signals, the digital steering signals, the other of the pulse trains and the serial pulse trains for combining the inputs to produce the drive signals or the servomechanism inputs. 